Certificate for #4881 ⟨a, b | abbbaaab=aba⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
• Auxiliary generators:
  1. aab=c

Axiom: abbbaaab=aba.

Referenced by [3].

Axiom: aab=c.

Defines rule #3.

Referenced by [3], [4], [7], [8], [11], [12], [14].

Overlap of [1] abbbaaab=aba with [2] aab=c:

Critical pair: abbbac=aba.

Defines rule #7.

Referenced by [4], [5], [7], [9], [13].

Overlap of [2] aab=c with [3] abbbac=aba:

Critical pair: aaba=cbbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [6], [8], [10].

Overlap of [3] abbbac=aba with [4] cbbac=ca:

Critical pair: abbbaca=ababbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [4] cbbac=ca with [4] cbbac=ca:

Critical pair: cbbaca=cabbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8].

Overlap of [3] abbbac=aba with [6] cabbac=caa:

Critical pair: abbbacaa=abaabbac.

Reduce LHS:

Reduce RHS:

Defines rule #13.

Referenced by [9], [14].

Overlap of [4] cbbac=ca with [6] cabbac=caa:

Critical pair: cbbacaa=caabbac.

Reduce LHS:

Reduce RHS:

Defines rule #9.

Referenced by [9], [10], [11], [12].

Overlap of [3] abbbac=aba with [8] caaa=ccbac:

Critical pair: abbbaccbac=abaaaa.

Reduce LHS:

Reduce RHS:

Defines rule #12.

Referenced by [13].

Overlap of [4] cbbac=ca with [8] caaa=ccbac:

Critical pair: cbbaccbac=caaaa.

Reduce LHS:

Reduce RHS:

Defines rule #6.

Overlap of [8] caaa=ccbac with [2] aab=c:

Critical pair: cac=ccbacb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [13].

Overlap of [8] caaa=ccbac with [2] aab=c:

Critical pair: caac=ccbacab.

Defines rule #4.

Overlap of [3] abbbac=aba with [11] ccbacb=cac:

Critical pair: abbbacac=abacbacb.

Reduce LHS:

Reduce RHS:

Defines rule #10.

Overlap of [7] abaaa=abcbac with [2] aab=c:

Critical pair: abac=abcbacb.

Flip LHS and RHS.

Defines rule #8.